Biotechnology has made it possible to collectgenome-wide observations to study properties of large biological systems. Sinceevents during cerebellar development are thought to occur sequentially in atightly controlled manner, itis reasonable to expect differential gene regulations during various stages of cerebellardevelopment. Therefore, we applied our comparative dynamic system modeling (DSM) framework to detect conserved anddifferential transcriptional interactions during mouse cerebellar development.

Wecollected substantial amount of time series gene expression data in developingmouse cerebella of BL6 and DB2 strains starting from E12 to E19 everyday andevery 3 days from P0 to P9 using the Illumina microarray platform. There weretwo or three replicates at each time point.  We hypothesized that some TFs play a major buttemporally non-uniform role in regulating gene expression during various stagesof cerebellar development.  Thus, weidentified a list of 1,235 known transcription factors (TFs) from a TF databaseto detectinteractions among them.  We first groupedthese TFs into 222 clusters by collinear dynamics in expression, because TFswith linearly correlated expression patterns cannot be differentiatedmathematically in DSM modeling. One representative gene was selected for eachcluster such that the representative minimized the median gene expression distanceto all other genes in the cluster.  Thenwe split the data into two parts: one part of data is time series from thedevelopmental event of tangential migration of GCP to EGL (from E12 to E15),the other part of data is from all other time points.  Then we detected conserved and differentialinteractions between cluster representatives by comparing these two parts ofdata using the comparative DSM framework. Considering both computational costsand the statistical power as supported by the available replicates, we searchedfor a maximum of one regulator for each TF. And the regulation patterns isallowed to have mathematical linear (βx_i)or sigmoid (βx_i²/(1+ x_i²)) form.Degradation is modeled as a linear factor. So for each TF (x_i), the regulation is expressed as dx_i/dt=β_ij x_j -β_i x_j  or  dx_i/dt=β_ij x_j²/(1+ x_j²) -β_i x_{i .}

The detectedinteractions were matched against BioGRID to identify any knowninteractions. BioGRID is an interaction database with more than 160,000 geneticinteractions derived from experimental results in various model organisms suchas Mus musculus and Rattus norvegicus. Matching against BioGRID waschecked for every pair of genes if each gene is in a different cluster of anyinteracting clusters. We also searched for indirectly interacting TFs butallowed only one intermediate gene between two TFs. Besides those interactions supported by BioGRID,other interactions suggested new hypotheses for transcriptional regulation.